However, they couldn't find a way back into the tie in the second half.
James Milner converted a penalty in first-half stoppage-time to lift the visitors, who were much improved after the interval but unable to produce the incisive moment they needed to level.
Jurgen Klopp could be handed a matchday ban by UEFA following his criticism of referee Szymon Marciniak after Liverpool's defeat to Paris Saint-Germain in the Champions League on Wednesday evening. Going into the game Klopp and his team knew a loss wouldn't knock them out, though a win could get rid of PSG from the competition.
Klopp's side have endured struggles away in Europe recently - losing four straight matches on the road - and while Tuchel praised his fellow German, he knows his team can make the most of home advantage.
Despite their enterprising start, the Parisian club were fortunate to keep all 11 players on the field after 25 minutes, as a Marco Verratti challenge on Joe Gomez, which resulted in a yellow card, could've been a red.
Substitutes: Alves (5), Choupo-Moting (6), Rabiot (N/A).
It is not what Klopp would have wanted having been top of Group C at the halfway stage but another electric Anfield night awaits.
Substitutes: Keita (5), Sturridge (5), Shaqiri (5). Liverpool need to win against Napoli and it's a goal difference shootout for qualification places and then away goals.
With Neymar it was even in the first half.
He will be required in the games to come, especially if Liverpool can overcome Napoli by two goals and escape their group.
MF Adrien Rabiot, NR - He was not lacking commitment when he was given five minutes towards the end and mucked in with everybody else as things got feisty.